Finite Group Databasebeta

← #13080003

Subgroups — #13080003

Order 1408.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#532C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3#10622704C212yesmaximal, complemented
4#10622688C212yesmaximal, complemented
5#10622655C214yesmaximal, complemented
6#10622632C212yesmaximal, complemented
7#10622620C212yesmaximal, complemented
8#10622537C211yesmaximal, characteristic, complemented
9C2×C11×#41—21no—
10C11×C4⋊Q8C2211yescharacteristic
11C11×#127C2211yescharacteristic
12C11×#124—21no—
13C11×#121—21no—
14C11×#121C2212yes—
15C4×D4×C11—21no—
16C4×D4×C11C2212yes—
17C2×C42×C11C2211yescharacteristic
18C2×#4324C2214yes—
19#66979—21no—
20#66977—21no—
21#66977C2212yes—
22C2×#4318C2212yes—
23#66923—21no—
24#66922C2211yescharacteristic
25#66922C2211yescharacteristic
26C4×Dic22—21no—
27C4×Dic22C2212yes—
28#66896C2214yes—
29#66874C2214yes—
30#66871C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32C4⋊(C11⋊C8)C2212yes—
33C11×#41—44no—
34C2×Q8×C11—21no—
35C2×D4×C11—22no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11C2312yes—
39C22×C4×C11—22no—
40C22×C4×C11D411yescharacteristic
41C22×C4×C11D411yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C2×Dic22—21no—
44C2×Dic22C2312yes—
45C11×C4⋊C4—21no—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—22no—
48C11×C22⋊C4—22no—
49C42×C11D411yescharacteristic
50C42×C11D411yescharacteristic
51C42×C11C2311yescharacteristic
52C42×C11C2311yescharacteristic
53C22⋊Dic11—22no—
54#4324—44no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61C4×Dic11—22no—
62#4318—42no—
63C2×C11⋊C8C2314yes—
64#3254—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11C2×D411yescharacteristic
67Q8×C11—42no—
68D4×C11—22no—
69D4×C11—22no—
70D4×C11—42no—
71D4×C11—44no—
72D4×C11—42no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—44no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—22no—
86C2×Dic11—22no—
87Dic22—22no—
88Dic22—22no—
89Dic22—42no—
90C11⋊C8—24no—
91#533—111no—
92#532D1111yescharacteristic
93#477—112no—
94#474—112no—
95#468—114no—
96#461—112no—
97#460—112no—
98#423—111no—
99C22×C11—21no—
100C22×C11—21no—
101C22×C11—21no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11C22×D411yescharacteristic
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—42no—
110C4×C11AGL(1,ℤ/8)12yes—
111C4×C11#13712yes—
112C4×C11H(5,𝔽2)11yescharacteristic
113C4×C112−1+411yescharacteristic
114Dic11—42no—
115Dic11—42no—
116C2×#41—21no—
117C2×SD16—114no—
118C2×M16—112no—
119C4⋊Q8—111no—
120C4⋊Q8—111no—
121C4⋊Q8C2×D1111yescharacteristic
122#127C2×D1111yescharacteristic
123#125—221no—
124#124—21no—
125C22⋊Q8—112no—
126C22⋊Q8—221no—
127#121—21no—
128#121C2×D1112yes—
129C4×Q8—112no—
130C4×Q8—221no—
131C4×D4—21no—
132C4×D4C2×D1112yes—
133#117—221no—
134C2×C42C2×D1111yescharacteristic
135#107—114no—
136C4⋊C8—112no—
137C4⋊C8—112no—
138#103—114no—
139#102—114no—
140C2×C11—41no—
141C2×C11—82no—
142C2×C11#53711yescharacteristic
143C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C11C2×#13711yescharacteristic
145#41—44no—
146C2×Q8—21no—
147C2×Q8—112no—
148C2×Q8—221no—
149C2×D4—22no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4C22×D1112yes—
153C22×C4—22no—
154C22×C4C22⋊D1111yescharacteristic
155C22×C4C22⋊D1111yescharacteristic
156C22×C4C22×D1111yescharacteristic
157SD16—444no—
158M16—442no—
159C2×C8—114no—
160C4⋊C4—21no—
161C4⋊C4—112no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C4⋊C4—222no—
165C4⋊C4—222no—
166C4⋊C4—221no—
167C4⋊C4C22×D1112yes—
168C22⋊C4—22no—
169C22⋊C4—22no—
170C22⋊C4—222no—
171C42—222no—
172C42C22⋊D1111yescharacteristic
173C42C22⋊D1111yescharacteristic
174C42C22×D1111yescharacteristic
175C42C22×D1111yescharacteristic
176C11#325411yescharacteristic, complemented, Sylow
177C23—22no—
178C23C2×C22⋊D1111yescharacteristic
179Q8—42no—
180Q8—222no—
181Q8—222no—
182Q8—442no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—44no—
187D4—42no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4C2×C22⋊D1111yescharacteristic
197C2×C4C2×C22⋊D1111yescharacteristic
198C2×C4C2×C22⋊D1111yescharacteristic
199C2×C4C2×C22⋊D1111yescharacteristic
200C2×C4C2×C22⋊D1111yescharacteristic
201C2×C4C23×D1111yescharacteristic
202C8—224no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22C22×C22⋊D1111yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—442no—
215C4—442no—
216C4#6698512yes—
217C4#6700412yes—
218C4#6704211yescharacteristic
219C4#6704311yescharacteristic
220C2—41no—
221C2—82no—
222C2C2×#6698511yescharacteristic
223C2C2×#6700411yescharacteristic
224C2#1062336411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#532C2
socleC22×C11C22×D4
hypercenter#532D11
hypocenterC11#3254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10623001C2semidirect
3. #10622704C2semidirect
4. #10622688C2semidirect
5. #10622655C2semidirect
6. #10622632C2semidirect
7. #10622620C2semidirect
8. #10622537C2semidirect
176. C11#3254semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#5322
#106230012
#106227042
#106226882
#106226552
#106226322
#106226202
#106225372
#325411